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Correct me if I'm wrong, but as far as I can tell the table listing the various chances of success with increasing number of dice is incorrect.
For instance, when you roll 3d6 the chance of at least one success is clearly 50% (3 * 1/6) not 42%, and so on.

It seems the table is listing the chances of only getting one success and discards the cases where more than one dice is a success.
At least to me this is quite misleading. 

Also the "Pushed Roll" column seems equally wrong. Pushing 1 dice should yield 33.34% chance (2 * 1/6) and not 29% in my mind.
As the heading is "chance of success" it would indicated that the first roll failed to get any successes. Pushing would then mean to roll all the dice once more.
The pushed roll column should therefore just be twice the "chance of success" column, as you get another chance with all your dice effectively doubling the dice pool.

.. or is it something I am missing here?

I’m no expert, but other people are, and I believe it’s 42% *edit* sorry I managed to delete a line. There are 75/216 ways of getting one 6, 15/216 ways of getting two 6s, and 1 way of getting three, so 75+15+1 = 91/216 ways of getting one or more sixes. Which equals 42.1%.

see this discussion about the dice probability table in Coriolis, which WAS wrong re pushed rolls. However it does confirm the result for non-pushed rolls:
http://forum.frialigan.se/viewtopic.php ... ity#p31726

But you alert me to another point, the push comes with an extra die, so I am not sure the pushed roll probabilities are correct. 

You are absolutely right!  I stand corrected. 

I didn't appreciate the difference between the chance to succeed and the number of successes. With multiple dice and more than one success is rolled, the roll is still only a success. So the probability space gets a bit truncated when more dice are added and we are looking at the chance to succeed, not the number of successes.
 
I should have paid more attention in class. Thanks for clearing this up!

Pushed is also going to vary based upon whether stress dice are in the base roll... because they can prevent pushing... and are a pin to figure because the number of dice rerolled is variable per permutation. It doesn't say the pool is increased, only that stress is, so I don't read it as adding an extra die...

So, doing a little math...
it looks like the table is correct for no stress dice in the initial pool and no added stress die.

Stress dice in the pool trim away some of the chances. The math is ugly, I don't feel like triple checking it, nor like writing the code to generate it accurately...